Question

A vector a of magnitude 8 units has two components. One is  perpendicular to a and is of magnitude

6 units. What is the magnitude of the other component?

[Hint: They are ‘components’ not ‘rectangular component’]​

Answer 1

Explanation:

Given A vector a of magnitude 8 units has two components. One is  perpendicular to a and is of magnitude 6 units. What is the magnitude of the other component?

• Let the vector be represented by vector PQ and the component by PR.
• Therefore second component will be RQ
• So vectors PQ = PR + RQ
• Also QR^2 = PQ^2 + PR^2
•                    = 8^2 + 6^2
•                    = 64 + 36
•                     = 100
•            Or QR = 10

Therefore magnitude of the other component is 10 units

Reference link will be

https://brainly.in/question/10130920

Answer 2

Magnitude of other component = 10 unit

Explanation:

Let say  Vector  a  is on   x  axis

then  Vector a  = 8 i

One component  is  perpendicular to a and is of magnitude 6 units.

=  6 j

Let say other component be  of magnitude b at angle α to x axis

=> bcosα i  + bsinαj

bcosα i  + bsinαj + 6 j =  8i

=> bcosα i  + bsinαj = 8i - 6j

=> bcosα = 8

   bsinα = - 6

Squaring both & adding then

b²cos²α + b²sin²α  = 8² + (-6)²

=> b²(cos²α +  sin²α ) = 64 + 36

=>  b² = 100

=> b = 10

Magnitude of other component = 10 units

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